How to choose which folders and files from the project to import into Subversion? When I do CVS - Import into version control - Import into Subversion, it simply imports the whole chosen folder. What if I don't want to import .idea folder and project-name.iml file for example? Is there a way to choose what to import?

VCS -> Enable Version Control Integration
or press Alt+Back Quote, and select Enable Version Control Integration....

In the Enable Version Control Integration dialog box that opens, select a version control system from the drop-down list that you want to associate with your project root.

From There your project will be associated with the version control system you want to use. You can the right click on the directories you do want to include in VCS and navigate to the Version control system. And then Add to VCS.

Even with the latest version of Intellij 2017, this is not a straight forward process to add a new project to Subversion.

As explained by 'another-programmer'
we need to first 'Share Directory' which is new project directory, by either using or creating a directory in subversion.
Then you should see the project files/directories turning green which means ready to check-in.
You can choose which files/dirs to check-in to your new project.